2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59499This note studies Arveson's curvature invariant for d-contractions specialized to the case d=1 of a single contraction operator on a Hilbert space. It establishes a formula which gives an easy-to-understand meaning for the curvature of a single contraction. The formula is applied to give an example of an operator with nonintegral curvature. Under the additional hypothesis that the contraction T be "pure", we show that its curvature K(T) is given by K(T) = - index(T) := -(dim ker T - dim coker T).LaTeX, 15 pagesOperator Algebras47A13 (Primary); 47A20 (Secondary)text